This invention relates to optically sampled delta-sigma analog-to-digital converters and more specifically to an optically sampled delta-sigma modulator.
It has been known for many years that delta-sigma modulation techniques can be used in analog-to-digital (A/D) converters. Only recently, however, have these techniques achieved widespread popularity. This popularity can be attributed to advances in VLSI technology that have allowed the realization of densely packed high speed circuits that are capable of effectively handling the bit stream associated with delta-sigma modulation.
A typical delta-sigma converter 100 is shown in FIG. 1A, and comprises a delta-sigma modulator 102 and a digital low-pass decimation filter 104. The delta-sigma modulator 102 comprises a summing node 111, an integrator 113 and a quantizer 115 coupled together in succession. A feedback loop 117 couples the output Y(i) of the delta-sigma modulator to the summing node 111 through a digital-to-analog (D/A) converter 112. In operation, an analog input signal that has been sampled X(i) enters the summing node 111 where an analog version of the feedback signal Ya(i) is subtracted from X(i) to create a difference signal Xd(i). The difference signal Xd(i) is then input to the integrator 113, which produces an integrated signal Xi(i). The quantizer then rounds the integrated signal Xi(i) to a closest possible level thereby producing a digital signal Y(i). The feedback loop 117 forces the average output of the modulator to be equal to the input signal X(i). The digital decimation filter 104 then processes the output stream of the delta-sigma modulator.
One byproduct of A/D conversion is quantization error. Quantization error occurs because the magnitude of the analog signals entering the quantizer can theoretically be equal to an infinite number of values, whereas the magnitude of the rounded signals leaving the quantizer can only be equal to a finite number of values. Therefore, the quantizer causes a rounding off, or quantization error.
The advantage of delta-sigma converters is their ability to reduce, relative to other types of converters, quantization error through the use of noise shaping and oversampling. Noise shaping is a filtering operation performed by the integrator 113 and feedback loop 117 that pushes the noise caused by the quantization error outside the bandwidth of interest. Oversampling performs the initial sampling operation at a rate much higher than twice the signal frequency. Then, when the quantized signal is processed by a lowpass decimation filter, much of the noise pushed to higher frequencies is removed by the filter.
Noise shaping will now be described with reference to the Z transform model of the delta-sigma modulator 102 shown in FIG. 1B. The integrator 113, often called the xe2x80x9cfeed forward loop filter,xe2x80x9d is a discrete time integrator having a transfer function of Zxe2x88x921/(1xe2x88x92Zxe2x88x921). Since the quantization noise is random, the quantizer 115 can be modeled as a noise source N(Z) coupled to a summing node 119. Moreover, the D/A converter 112 can be treated as ideal, and modeled as a unity gain transfer function for a single bit D/A converter. The output of the modulator is then given by:
Y(Z)=X(Z)Zxe2x88x921+N(Z)(1xe2x88x92Zxe2x88x921)
Thus, the transfer function for the input signal, Hx(Z), is equal to Zxe2x88x921, and the transfer function of the noise source, Hn(Z), is equal to (1xe2x88x92Zxe2x88x921). Since zero frequency is represented in the Z transform at Z=1, it can readily be seen that, as the frequency approaches zero, N(Z) is attenuated. Therefore, the delta-sigma modulator acts as a high pass filter for quantization noise, and a low pass filter for the input signal.
The second way that delta sigma modulators reduce quantization noise is through oversampling. It is well known that to recover a sampled analog signal, the signal must be sampled at a rate greater than or equal to twice the signal frequency. Oversampling refers to sampling the signal at a rate much greater than twice the signal frequency. FIG. 2A shows the magnitude of quantization noise, in terms of the signal-to-noise ratio (SNR), at a particular frequency of interest f when the analog signal is sampled at the minimum sampling rate of fs. FIG. 2B shows the magnitude of quantization noise at the same frequency of interest f when the signal is sampled at a sampling rate equal to 2fs. By comparing the quantization noise in FIGS. 2A and 2B, respectively, one can see that increasing the sampling frequency spreads the quantization noise over a larger bandwidth because the total amount of quantization noise remains the same over the different sampling bandwidths. Thus, increasing the sampling rate relative to twice the signal frequency, or oversampling, reduces the quantization noise in the bandwidth of interest.
One factor that limits the performance of analog-to-digital converters is temporal jitter in the sampling clock. Sampling clock jitter results in non-uniform sampling and increases the total error power in the quantizer output. If the clock jitter is assumed to contribute white noise, the total power of the error is reduced in a delta-sigma A/D converter by the oversampling ratio. Nevertheless, the clock jitter still can be a limiting factor for conversion of wideband signals.
One way to overcome sampling jitter limitations is through optical sampling. Optical sampling makes use of very short laser pulses with high temporal stability to sample an analog electrical input. Subpicosecond sampling, or aperture windows and sampling-pulse repetition rates above 40 GHz, can be achieved with optical sampling. The jitter of the optical sampling pulses can be less than 10 fsecs.
A conventional optically sampled A/D converter 200 is shown in FIG. 3. A series of optical impulses 201 from a mode-locked laser 203 are applied to an electro-optic modulator 205. The analog electrical input X(t) is also applied to the modulator 205. The optical impulses 201 sample the voltage associated with the analog electrical input X(t). The resultant optical pulses 207, with intensities determined by the modulator 205 voltage, are fed to a photodetector 209. The photodetector 209 electrical output 211 is supplied as the input of an electronic quantizer 212.
The above approach achieves very high sampling rates because the pulse repetition rate of the mode-locked laser can be 40 GHz or higher. Even higher repetition rates for the optical sampling pulses can be achieved by combining several time-delayed copies of each laser pulse.
A photonic sampler can be combined with a discrete-time delta-sigma modulator, as illustrated in FIG. 3, by replacing the electronic quantizer 212 with such a discrete-time modulator. Typical discrete-time delta-sigma modulators are implemented as switched-capacitor networks, since these circuits provide good control and flexibility in the realization of the noise-shaping and signal-transfer functions. The sampling rate of such switched-capacitor implementations, however, is limited to one-half or less of the unity gain bandwidth of its operational amplifiers. Also, such implementations typically are compatible only with CMOS transistor technologies.
For high sampling rates, continuous-time delta-sigma modulators are used. The sampling rates of such modulators can be greater than the unity gain bandwidth of its integrators. Also, such continuous-time modulators can be implemented in high speed transistor technologies such as heterojunction bipolar transistors formed in InP or GaAs materials. In a typical continuous-time delta-sigma modulator, the sampling occurs at the quantizer. A typical quantizer consists of an electronic latched comparator, which acts as a track and compare amplifier. In such an implementation, the sampling interval can depend on the input signal to the quantizer. The minimum sampling interval can be considered to be some portion of an edge of the clock waveform. The sampling interval, however, can become a large fraction of the clock period if the input level is approximately the same as the reference level. This results in additional uncertainty in the sampling. Thus, there is a need to incorporate an optical sampler into a continuous-time delta-sigma modulator.
An example of an optically sampled delta-sigma A/D converter, previously described by P. E. Pace and J. P. Powers of the U.S. Naval Postgraduate School, is illustrated in FIG. 4. This delta-sigma converter 300 contains a mode-locked fiber laser 302 to act as the source of sampling pulses, and two photonic samplers 304, which are Mach-Zehnder interferometric modulators. The fiber lattice structure 306 acts as an optical integrator. The photonic samplers 304 also serve as the analog summing point at the input of the delta-sigma loop.
Difficulties associated with the A/D converters shown in FIGS. 3 and 4 include high non-linearity and distortion spurs. Thus, the dynamic range of the photonic sampler limits prior A/D converters using photonic sampling techniques. For example, an analog waveform with a 5 GHz bandwidth can only be sampled to a resolution of 7.5 bits because the spur-free dynamic range of such samplers is approximately 110 dB-Hz⅔. Therefore, what is needed is an A/D converter system that can utilize optical sampling without being adversely affected by the noise and distortion from the photonic sampler.
The present invention overcomes the difficulties associated with optical sampling by integrating the photonic sampler within the loop of a delta-sigma architecture by placing it after a continuous time integrator and before the electronic quantizer, thereby applying the noise shaping to spurs and noise which are produced by the photonic sampler. Moreover, since the dynamic range of the photonic sampler only needs to be as great as that of the quantizer, which typically can discern only one or a few bits, the photonic sampler can be a very nonlinear device such as an electro-absorption photodetector, which otherwise could not be used for sampling. Oversampling and noise shaping can therefore be employed to greatly increase the resolution of an A/D converter beyond the dynamic range of the photonic sampler or quantizer.
In one aspect the invention provides a delta-sigma modulator comprising: means for generating an analog feedback signal from a digital signal; means for producing a first difference signal, said first difference signal being equal to a difference in magnitude between a first analog signal and the analog feedback signal; means for integrating the first difference signal, thereby producing a first integrated signal; means for photonically sampling the first integrated signal, thereby producing a sampled integral signal; and means for quantizing the sampled integral signal, thereby producing the digital signal.
In one aspect the invention provides a method of performing delta sigma modulation comprising the steps of: producing a first difference signal equal to the difference in magnitude between a first analog signal and an analog feedback signal generated from a digital signal; integrating the first difference signal, thereby producing a first integrated signal; sampling the integral signal, thereby producing a sampled integral signal; quantizing the sampled integral, thereby producing the digital signal.
In another aspect the invention provides a delta-sigma modulator comprising: a first node which produces a difference signal equal to the difference in magnitude between a continuous time analog signal and an analog feedback signal generated from a digital output signal; an integrator, coupled to the first node, which integrates the difference signal and produces a first integrated signal; a sampler, coupled to the integrator, which samples the first integrated signal and produces a sampled integral signal; a quantizer, coupled to the sampler, which quantizes the sampled integral signal and produces the digital output signal; wherein an output of the quantizer is coupled to the first node through a digital to analog converter.
In another embodiment, multiple photonic samplers can be incorporated in parallel delta-sigma AND converter architecture, thereby achieving improvements in resolution with little or no oversampling.
In another embodiment, a delta sigma modulator comprising: a plurality of parallel connected circuits, each circuit being connected to receive a continuous time analog signal and comprising: a modulator for modulating the continuous time analog signal according to a coded sequence to produce a modulated analog signal; a first node to produce a difference signal equal to a difference in magnitude between the modulated analog signal and an analog feedback signal generated from a digital signal; an integrator, coupled with the first node, to integrate the difference signal, thereby producing a first integrated signal; at least one sampler, coupled with the integrator, to sample the first integrated signal, thereby producing a sampled integral signal; at least one quantizer, coupled with the sampler, to quantize the sampled integral signal, thereby producing the digital signal, an output of the quantizer being coupled to the first node through a digital to analog converter; and a digital demodulator for demodulating the digital signal; and wherein the digital signals produced by said parallel connected circuits are summed at a summing device.
In another embodiment, a delta sigma-modulator of Y order, where Y is an integer greater than or equal to one, said delta-sigma modulator comprising: a set of Y nodes, said set of Y nodes being divided into a first subset and a second subset when Y is greater than or equal to two, each node producing a difference signal equal to a difference between a first signal and a second signal, said first signal being equal to an analog input into said delta-sigma modulator when one node in said set of Y nodes is a first node, said second signal being equal to a feedback signal generated from a digital output signal for said first subset of Y node; a set of Y integrators, said set of Y integrators being coupled with said set of Y nodes, each integrator integrating the difference signal from a preceding node in said set of Y nodes, said integrated signal being directed toward a proceeding node from said set of Y nodes until said integrated signal is generated from a last integrator from said set of Y integrators, said last integrator producing a last integrated signal; a set of K summer devices, where K is an integer greater than or equal to Y/2, K being equal to zero when Y is equal to 1, each one of said set of K summers being connected with said nodes in said second subset of Y nodes, each of said summers combining a feedback signal generated from said digital output signal with the integrated signal from one of said set of Y integrators; a photonic sampler, for photonically sampling said last integrated signal and producing a sampled integrated signal; a quantizer, which quantizes the sampled integrated signal and produces the digital output signal; and a set of Y digital to analog converters, each digital to analog converter for converting said digital output signal into said feedback signal, a first subset of Y digital to analog converters providing said feedback signals to said first subset of Y nodes, a second subset of Y digital to analog converters providing said feedback signals to said set of K summers.
In another embodiment, a method for improving a delta-sigma modulator comprising the steps: integrating an analog input signal producing an integrated analog input signal; and optically sampling said integrated analog input signal to produce an optically sampled integrated signal.